degrees,g Segments Theorem
given a segment with points A,B,C and D arranged as shown, the following statements are true
1. if AB=CD, then AC=BD. a_b_c_d 2. if AC=BD, then AB=CD.
Addition Property- If a = b, then a+c = b+c
Subtraction Property- If a = b, then a - c = b - c
Multiplication Property- If a = b, then ac = bc
Division Property- If a =b and c doesnt = 0 the a/c = b/c
Reflexive property- for any real number a, a = a
Symmetric Property- for all real numbers a and b, if a=b then b=a
Transitive Property- for all real numbers a,b,and c, if a=b, and b=c then a=b
Substitution Property- if a=b you can replace a with b in any true equation with a and the resulting equation will be true
Overlapping segments theorem- it AB=CD then AC=BD
If AB=CD then BC=AD
Equivalence Properties of Equality:
Reflexive property-for any real number a, a=a.
Symmetric property- for all real numbers a and b, if a=b then b=a.
Transitive property- for all real numbers a,b and c if a=b and b=c then a=c Overlapping Angles Theorem: Given angle AOD with points B and C in its interior, the following statements are true: if the measure of angle AOB equals the measure of COD, then the measure AOD equals 90 degrees.
Vertical Angles theorem 2.5.1: If there are two angles vertical to eachother, they are congruent
Solve and write a reason for each step:
10 -2x=3(x-2)+4 Given
10-2x=3x-6+4 Distributive
+ 2 +2
10 = 5x-6+4 Addition
-4 -4 Simplify
10 = 5x - 2
+2 +2 Addition
12 5x
---- = ----- Division
5 5
x= 12/5 If equals are added to equals, then the wholes are equal.__
x - 3 = 5 x - 3 + 3 = 5 + 3 x = 8
Congruence like the relation of equality, satisfies the equivalence properties.Any relation that satisfies these three equivalence properties is called equivalence relation.
given a segment with points A,B,C and D arranged as shown, the following statements are true
1. if AB=CD, then AC=BD. a_b_c_d
2. if AC=BD, then AB=CD.
Addition Property- If a = b, then a+c = b+c
Subtraction Property- If a = b, then a - c = b - c
Multiplication Property- If a = b, then ac = bc
Division Property- If a =b and c doesnt = 0 the a/c = b/c
Reflexive property- for any real number a, a = a
Symmetric Property- for all real numbers a and b, if a=b then b=a
Transitive Property- for all real numbers a,b,and c, if a=b, and b=c then a=b
Substitution Property- if a=b you can replace a with b in any true equation with a and the resulting equation will be true
Overlapping segments theorem- it AB=CD then AC=BD
If AB=CD then BC=AD
Equivalence Properties of Equality:
Reflexive property-for any real number a, a=a.
Symmetric property- for all real numbers a and b, if a=b then b=a.
Transitive property- for all real numbers a,b and c if a=b and b=c then a=c
Overlapping Angles Theorem: Given angle AOD with points B and C in its interior, the following statements are true: if the measure of angle AOB equals the measure of COD, then the measure AOD equals 90 degrees.
Vertical Angles theorem 2.5.1: If there are two angles vertical to eachother, they are congruent
Solve and write a reason for each step:
10 -2x=3(x-2)+4 Given
10-2x=3x-6+4 Distributive
+ 2 +2
10 = 5x-6+4 Addition
-4 -4 Simplify
10 = 5x - 2
+2 +2 Addition
12 5x
---- = ----- Division
5 5
x= 12/5
If equals are added to equals, then the wholes are equal.__
x - 3 = 5
x - 3 + 3 = 5 + 3
x = 8
Congruence like the relation of equality, satisfies the equivalence properties.Any relation that satisfies these three equivalence properties is called equivalence relation.